The siding looks like its not one flat piece but made of multiple flat layers? There are different siding installment methods. What does this one look like?
Your siding is shiplap, you can see that the grain pattern continues from the face of the board onto the lapped edge. Normally the boards are milled so that the faces fit close together, so it could be called "lap and gap" for clarity. I've no idea if that's a regional term or not.
If it had actually been made of two layers it would be board and batten, which may offer you some visually similar style products in your search. Traditionally though the batts are much smaller than the boards, and the siding is installed vertically to shed water.
I would call that "shiplap" (but some will refer to it as tongue & groove), but names may differ based on location.
The idea of the joint is so that water does not stay on the joint between the two planks, but falls away.
We have that on our house and around here it is called lap and gap. I have replaced some rotted courses and had to go to a lumberyard to get what I wanted. I have examined this type of siding in detail.
Ship lap siding is installed without gaps, but there will be grooves. Lap and gap has a much longer lap on one end resulting in a distinctive wide horizontal gap. Some (lap and gap) siding can be installed with the rough side out to give lap and gap, but if installed with the smooth side out the result is no gap outside giving the effect of ship lap. However, there will be an internal gap. I would think that ship lap would have only a very narrow gap or no gap, just a groove.
Look at the design of the planks in the link.